What is compactness?

Some articles on compactness:

Limit Point Compact
... In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent ... For general topological spaces, however, these three notions of compactness are not equivalent ...
Strongly Compact Cardinal
... than κ then κ is strongly compact if its logic satisfies an analog of the compactness property of finitary logic ... The property of strong compactness may be weakened by only requiring this compactness property to hold when the original collection of statements has ... Strong compactness implies measurability, and is implied by supercompactness ...
Barwise Compactness Theorem
... In mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theorem for first-order logic to ...
Cover (topology) - Compactness
... language of covers is often used to define several topological properties related to compactness ...

More definitions of "compactness":

  • (noun): The consistency of a compact solid.